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Home/Chain Registry/Block #2,293,509

Block #2,293,509

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/12/2017, 2:27:40 PM Β· Difficulty 10.9541 Β· 4,549,648 confirmations

1CC
Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header
Block Hash
a56bac43c9205c82c48f044a1b86d815d0d0056843cfa2201849357cfcd8ad03
View on Chainz β†—

Difficulty

10.954125

Transactions

1

Size

199 B

Version

2

Bits

0af44181

Nonce

910,120,861

Timestamp

9/12/2017, 2:27:40 PM

Confirmations

4,549,648

Merkle Root

5a99b8b7602d46a0446bc8389cee80fb683eb7559952f8366fec47021cb1a754
Transactions (1)
Coinbase5a99b8b7602d46…ec47021cb1a754
1 in β†’ 1 out8.3200 XPM109 B
AS16vtpw…rmZvQoFC
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

4.328 Γ— 10⁹³(94-digit number)
43283829658826151266…56675693201419363120
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin βˆ’ 1
4.328 Γ— 10⁹³(94-digit number)
43283829658826151266…56675693201419363119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.656 Γ— 10⁹³(94-digit number)
86567659317652302533…13351386402838726239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.731 Γ— 10⁹⁴(95-digit number)
17313531863530460506…26702772805677452479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.462 Γ— 10⁹⁴(95-digit number)
34627063727060921013…53405545611354904959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.925 Γ— 10⁹⁴(95-digit number)
69254127454121842026…06811091222709809919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.385 Γ— 10⁹⁡(96-digit number)
13850825490824368405…13622182445419619839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.770 Γ— 10⁹⁡(96-digit number)
27701650981648736810…27244364890839239679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.540 Γ— 10⁹⁡(96-digit number)
55403301963297473621…54488729781678479359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.108 Γ— 10⁹⁢(97-digit number)
11080660392659494724…08977459563356958719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.216 Γ— 10⁹⁢(97-digit number)
22161320785318989448…17954919126713917439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.432 Γ— 10⁹⁢(97-digit number)
44322641570637978897…35909838253427834879
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11
How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 2293509

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock a56bac43c9205c82c48f044a1b86d815d0d0056843cfa2201849357cfcd8ad03

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #2,293,509 on Chainz β†—
Circulating Supply:57,989,622 XPMΒ·at block #6,843,156 Β· updates every 60s
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